A particle moves in a straight-line OA; the distance of the particle from O at time t seconds is x ft, where x = a + bt + ct^2 (a, b > 0). What is the meaning of the constant c?

(a) Uniform acceleration

(b) Non – uniform acceleration

(c) Uniform retardation

(d) Non – uniform retardation

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The question is from Calculus Application in section Application of Calculus of Mathematics – Class 12

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Correct answer is (a) Uniform acceleration

For explanation: We have, x = a + bt + ct^2 ……….(1)

Let, v and f be the velocity and acceleration of a particle at time t seconds.

Then, v = dx/dt = d(a + bt + ct^2)/dt = b + ct ……….(2)

And f = dv/dt = d(b + ct)/dt = c ……….(3)

Since f = dv/dt = c, hence, c represents the uniform acceleration of the particle.